Finite Group Databasebeta

← #352×D151 #34070744

Subgroups — #352×D151 #34070744

Order 19328.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#123×D151C211yesmaximal, characteristic
2#100×D151C211yesmaximal, characteristic
3#99×D151C211yesmaximal, characteristic
4#23752003C211yesmaximal, characteristic, complemented
5#23752002C211yesmaximal, characteristic, complemented
6#23752001C211yesmaximal, characteristic, complemented
7#352×C151C211yesmaximal, characteristic, complemented
8C2×D4×D151C2211yescharacteristic
9C22×C4×D151C411yescharacteristic, complemented
10M16×D151—21no—
11#18012724—21no—
12#18012723C411yescharacteristic, complemented
13#18012722C411yescharacteristic, complemented
14#18012721—21no—
15#18012720C2211yescharacteristic
16C4⋊C4×D151—21no—
17C22⋊C4×D151—21no—
18C22⋊C4×D151—21no—
19C22⋊C4×D151C411yescharacteristic, complemented
20#18012656C2211yescharacteristic
21#18012655—21no—
22#18012654C2211yescharacteristic
23#18012653—21no—
24#123×C151C2211yescharacteristic
25#100×C151C2211yescharacteristic
26#99×C151C2211yescharacteristic
27C23×D151C2×C411yescharacteristic
28C23×D151D411yescharacteristic
29C2×D604D411yescharacteristic
30C2×C22⋊D151C2×C411yescharacteristic
31C2×C22⋊D151D411yescharacteristic
32D4×D151—41no—
33D4×D151—41no—
34C22×Dic151C2×C411yescharacteristic, complemented
35C2×C4×D151—21no—
36C2×C4×D151—21no—
37C2×C4×D151—21no—
38C2×C4×D151—41no—
39C2×C4×D151—41no—
40C2×C4×D151—41no—
41C2×C4×D151D411yescharacteristic
42#14558988—21no—
43#14558987—41no—
44C8×D151—41no—
45C4⋊Dic151—21no—
46Dic151⋊C4—21no—
47Dic151⋊C4—21no—
48C22⋊Dic151—21no—
49C22⋊Dic151—21no—
50C22⋊Dic151C2×C411yescharacteristic, complemented
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—21no—
53(C2×D151)⋊C4—21no—
54(C2×D151)⋊C4—41no—
55C2×D4×C151C2311yescharacteristic
56C22×C4×C151C2×C411yescharacteristic, complemented
57M16×C151—21no—
58C4⋊C4×C151—21no—
59C22⋊C4×C151—21no—
60C22⋊C4×C151—21no—
61C22⋊C4×C151C2×C411yescharacteristic, complemented
62C22×D151—21no—
63C22×D151—21no—
64C22×D151—21no—
65C22×D151—21no—
66C22×D151—42no—
67C22×D151—42no—
68C22×D151C22⋊C411yescharacteristic
69C22×D151C22⋊C411yescharacteristic
70C22×D151C22⋊C411yescharacteristic
71D604—41no—
72C22⋊D151—41no—
73C22⋊D151—41no—
74C2×Dic151—21no—
75C2×Dic151—21no—
76C2×Dic151—41no—
77C2×Dic151—41no—
78C2×Dic151C22⋊C411yescharacteristic
79C4×D151—21no—
80C4×D151—21no—
81C4×D151—42no—
82C4×D151—42no—
83C4×D151—41no—
84C4×D151—41no—
85C4×D151—82no—
86C151⋊C8—41no—
87C23×C151C22×C411yescharacteristic
88C23×C151C2×D411yescharacteristic
89D4×C151—41no—
90C2×C4×C151—21no—
91C2×C4×C151—21no—
92C2×C4×C151—41no—
93C2×C4×C151—41no—
94C2×C4×C151C2×D411yescharacteristic
95C8×C151—41no—
96C22×C151—21no—
97C22×C151—21no—
98C22×C151—41no—
99C22×C151—41no—
100C22×C151C2×C22⋊C411yescharacteristic
101C2×D151—22no—
102C2×D151—21no—
103C2×D151—21no—
104C2×D151—42no—
105C2×D151—42no—
106C2×D151—42no—
107C2×D151—41no—
108C2×D151—41no—
109C2×D151—81no—
110C2×D151#9911yescharacteristic
111C2×D151#9911yescharacteristic
112C4×C151—21no—
113C4×C151—41no—
114C4×C151—41no—
115C4×C151—81no—
116Dic151—21no—
117Dic151—41no—
118Dic151—41no—
119Dic151—81no—
120C2×C151—21no—
121C2×C151—41no—
122C2×C151—41no—
123C2×C151C2×#9911yescharacteristic
124D151—21no—
125D151—41no—
126D151—41no—
127D151#35212yesdirect product factor
128C151C2×#35211yescharacteristic, complemented, Sylow
129C2×#352—1511nomaximal, Sylow
130C2×#123—1511no—
131C2×#100—1511no—
132C2×#99—1511no—
133#352—1511no—
134#352—1511no—
135#352—1511no—
136#352D15111yescharacteristic, direct product factor
137C22×D4—1511no—
138C23×C4—1511no—
139C2×M16—3021no—
140#123—3021no—
141#123—3021no—
142#123—1511no—
143#123—1511no—
144#123—1511no—
145#123C2×D15111yescharacteristic
146C2×C4⋊C4—3021no—
147C2×C22⋊C4—3021no—
148C2×C22⋊C4—3021no—
149C2×C22⋊C4—1511no—
150#100—3021no—
151#100—1511no—
152#100C2×D15111yescharacteristic
153#99—3021no—
154#99—1511no—
155#99C2×D15111yescharacteristic
156C24—1511no—
157C24—1511no—
158C2×D4—6041no—
159C2×D4—6041no—
160C2×D4—1511no—
161C2×D4—1511no—
162C2×D4—1511no—
163C2×D4C22×D15111yescharacteristic
164C22×C4—3021no—
165C22×C4—3021no—
166C22×C4—3021no—
167C22×C4—6041no—
168C22×C4—6041no—
169C22×C4—6041no—
170C22×C4—1511no—
171C22×C4—1511no—
172C22×C4C4×D15111yescharacteristic, complemented
173M16—21no—
174M16—3021no—
175M16—6041no—
176C2×C8—6041no—
177C4⋊C4—21no—
178C4⋊C4—3021no—
179C4⋊C4—3021no—
180C4⋊C4—3021no—
181C22⋊C4—21no—
182C22⋊C4—21no—
183C22⋊C4—3021no—
184C22⋊C4—3021no—
185C22⋊C4—3021no—
186C22⋊C4—3021no—
187C22⋊C4—3021no—
188C22⋊C4—6041no—
189C22⋊C4—1511no—
190C22⋊C4C4×D15111yescharacteristic, complemented
191C23—3021no—
192C23—3021no—
193C23—3021no—
194C23—3021no—
195C23—6042no—
196C23—6042no—
197C23—1511no—
198C23—1511no—
199C23—1511no—
200C23C2×C4×D15111yescharacteristic
201C23D4×D15111yescharacteristic
202D4—41no—
203D4—6041no—
204D4—6041no—
205D4—6041no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—3021no—
211C2×C4—3021no—
212C2×C4—3021no—
213C2×C4—3021no—
214C2×C4—6042no—
215C2×C4—6042no—
216C2×C4—6041no—
217C2×C4—6041no—
218C2×C4—6041no—
219C2×C4—6041no—
220C2×C4—1511no—
221C2×C4—12082no—
222C2×C4D4×D15111yescharacteristic
223C8—41no—
224C8—6041no—
225C22—21no—
226C22—21no—
227C22—41no—
228C22—41no—
229C22—3022no—
230C22—3021no—
231C22—3021no—
232C22—6041no—
233C22—6041no—
234C22—6042no—
235C22—6042no—
236C22—6042no—
237C22—1511no—
238C22—1511no—
239C22—12081no—
240C22C22⋊C4×D15111yescharacteristic
241C4—21no—
242C4—41no—
243C4—41no—
244C4—81no—
245C4—3021no—
246C4—6041no—
247C4—6041no—
248C4—12081no—
249C2—21no—
250C2—41no—
251C2—41no—
252C2—3021no—
253C2—6041no—
254C2—6041no—
255C2—1512no—
256C2#99×D15111yescharacteristic
subgroupG/H
centerC2#99×D151
commutatorC23×C151C22×C4
FrattiniC2×D4C22×D151
Fitting#352×C151C2
socleC2×C151C2×#99
prime radicalC2×D4×D151C22
cosocleC2×D4×C151C23
hypercenter#352D151
hypocenterC151C2×#352
LCSG ▷ C23×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #23752003C2semidirect
5. #23752002C2semidirect
6. #23752001C2semidirect
7. #352×C151C2semidirect
9. C22×C4×D151C4semidirect
12. #18012723C4semidirect
13. #18012722C4semidirect
19. C22⋊C4×D151C4semidirect
34. C22×Dic151C2×C4semidirect
50. C22⋊Dic151C2×C4semidirect
56. C22×C4×C151C2×C4semidirect
61. C22⋊C4×C151C2×C4semidirect
127. D151#352direct (N × H)
128. C151C2×#352semidirect
136. #352D151direct (N × H)
172. C22×C4C4×D151semidirect
190. C22⋊C4C4×D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#123×D1512
#100×D1512
#99×D1512
#237520032
#237520022
#237520012
#352×C1512
C2×#352151